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Residual entropy is the difference in entropy between a non-equilibrium state and crystal state of a substance close to absolute zero.This term is used in condensed matter physics to describe the entropy at zero kelvin of a glass or plastic crystal referred to the crystal state, whose entropy is zero according to the third law of thermodynamics.
The quantile function, Q, of a probability distribution is the inverse of its cumulative distribution function F. The derivative of the quantile function, namely the quantile density function, is yet another way of prescribing a probability distribution. It is the reciprocal of the pdf composed with the quantile function.
The residual entropy of a fluid has some special significance. In 1976, Yasha Rosenfeld published a landmark paper, showing that the transport coefficients of pure liquids, when expressed as functions of the residual entropy, can be treated as monovariate functions, rather than as functions of two variables (i.e. temperature and pressure, or ...
Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy. Generally, information entropy is the average amount of information conveyed by an event, when considering all ...
where () is the binary entropy function [1] = () () In probability theory and statistics , the logistic distribution is a continuous probability distribution . Its cumulative distribution function is the logistic function , which appears in logistic regression and feedforward neural networks .
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
Relative entropy relates to "rate function" in the theory of large deviations. [24] [25] Arthur Hobson proved that relative entropy is the only measure of difference between probability distributions that satisfies some desired properties, which are the canonical extension to those appearing in a commonly used characterization of entropy. [26]
The derivative of the quantile function, the quantile density function, for the Cauchy distribution is: ′ (;) = [()]. The differential entropy of a distribution can be defined in terms of its quantile density, [13] specifically: